Todd carded five birdies on the back nine, including one each on the 17th and 18th holes, to post a six-under 64 at the TPC Four Seasons on Friday.
That was enough for the 28-year-old American to move two shots clear at the top of the leaderboard at the PGA Tour event, with Martin Kaymer of Germany, Canadian pair Graham DeLaet and Mike Weir, England's Paul Casey, Australian Marc Leishman, Morgan Hoffmann, Tim Herron and Charles Howell III all tied for second.
Sweden's Peter Hanson, who had held a one-stroke lead after the first round, shot a three-over 73 to plummet to a tie for 25th at two-under overall.
Speaking after the second round in Texas, Todd was thrilled to be challenging for a PGA Tour title in just his second season on the United States' premier golf tour - and his first since 2009.
"It's nice to put two under-par rounds together before the cut," Todd told PGATour.com.
"That's been a challenge for me this year."
Todd's best result so far this season was at the Texas Open, where he finished in a tie for sixth, but he has missed the cut in three of his past seven events.
After starting the Byron Nelson Championship with a two-under 68, Todd was solid if unspectacular over the first six holes of his second round in Irving, but consecutive birdies on the seventh and eighth holes saw the Pittsburgh-born golfer move under par for the day.
Birdies followed on the 10th, 11th and 13th holes before Todd bogeyed the par-four 15th.
The bogey was barely a blip on the radar, however, as superb approach shots on the final two holes yielded birdies and saw Todd finish the round at eight-under overall.
Kaymer, who won last week's The Players Championship, started on the back nine on Friday and notched his second straight round of 67 to join seven others at six under.
Of those, Casey produced the best score with his seven-under 63 the round of the day.
The 36-year-old Englishman had shot a 71 on the opening day and looked set for more pain when he bogeyed the third and fifth holes.
An eagle on the seventh saw Casey arrest his slide, although he then bogeyed the ninth hole, before storming home with six birdies and an eagle on the back nine.
Gary Woodland, Boo Weekley and Ryan Palmer, plus South African duo Retief Goosen and Tyrone Van Aswegen, sit on five under in a share of 10th position.